阿基米德晶格与拉夫斯晶格上的经典偶极海森堡模型
Classical dipolar Heisenberg models on the Archimedean and Laves lattices
- CRISP – Centre de Recerca Independent de sa Pobla（萨波布拉独立研究中心）
- Universitat de les Illes Balears（巴利阿里群岛大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究系统计算了15种阿基米德与拉夫斯平面晶格上经典偶极海森堡模型的基态与自旋波谱，揭示了倾斜行为、量子修正与晶格几何的关联，为相关材料与人工磁体实验提供预测。
AI中文摘要：
我们研究了11种阿基米德平面晶格和8种拉夫斯平面晶格在标准几何结构下，通过偶极-偶极相互作用耦合的经典海森堡自旋，这些晶格可归为15个不同的顶点集合。针对每种晶格，我们计算了傅里叶空间相互作用矩阵$\tilde{A}(\bk)$，提取了卢廷格-蒂萨有序波矢$\bk_{0}$，通过在共 commensurate 磁胞上进行无约束最小化确定了经典基态，并评估了沿（磁）布里渊区高对称路径的线性化自旋波色散$\tilde{\tau}_{i}(\bk)$以及霍尔斯坦-普里马科夫矩约化。\n基态可分为三类：5种为共线结构，2种为与晶格对称性共格的非共线角度结构，8种以超越数角度倾斜，我们将这些角度精确计算到30位有效数字。在整个晶格家族中，卢廷格-蒂萨强条件的失效与非共格倾斜的出现完全吻合，双向均无例外。截断相互作用作用程的结果表明，晶格是否发生倾斜由局域配位几何决定，而倾斜角的大小由长程尾部相互作用设定。\n量子修正由磁基矢大小决定的磁振子谱主导，与阻挫无关，因此阻挫分类与涨落分类相互独立；角共享晶格具有最窄的低能分支。这些结果构成了全部1-均匀平面铺砌及其对偶晶格上偶极海森堡系统的谱图集，可为磁性离子占据阿基米德或拉夫斯晶格的材料的非弹性中子散射实验，以及偶极耦合纳米磁体人工阵列提供预测。
英文摘要：
We study classical Heisenberg spins interacting through the dipole--dipole interaction on the eleven Archimedean and eight Laves planar lattices at canonical geometry, which reduce to fifteen distinct vertex sets. For each lattice we compute the Fourier-space interaction matrix $\Am(\bk)$, extract the Luttinger--Tisza ordering wave vector $\bk_{0}$, determine the classical ground state by unconstrained minimization on the commensurate magnetic cell, and evaluate the linearized spin-wave dispersion $\varepsilon_{i}(\bk)$ along the high-symmetry path of the (magnetic) Brillouin zone together with the Holstein--Primakoff moment reduction. The ground states fall into three classes: five are collinear, two are non-collinear at angles commensurate with the lattice symmetry, and eight cant at transcendental angles, which we determine to thirty digits. Across the family, failure of the Luttinger--Tisza strong condition coincides exactly with the appearance of incommensurate canting, with no exceptions in either direction. Truncating the interaction range shows that whether a lattice cants is fixed by the local coordination geometry, whereas the value of the canting angle is set by the long-range tail. The quantum corrections are governed by the magnon spectrum through the size of the magnetic basis and are uncorrelated with frustration, so that the frustration and fluctuation classifications are independent; the corner-sharing lattices host the narrowest low-energy branches. The results constitute a spectral atlas of dipolar Heisenberg systems on the full family of $1$-uniform planar tilings and their duals, and provide predictions for inelastic neutron scattering in materials whose magnetic ions occupy Archimedean or Laves lattices, and for artificial arrays of dipolar-coupled nanomagnets.
